Projection in the situation calculus refers to answering queries about the future evolutions of the modeled domain, while progression refers to updating the logical representation of the initial state so that it reflects the changes due to an executed action. In the general case projection is not decidable and progression may require second-order logic. In this paper we focus on a recent result about the decidability of projection and use it to drive results for the problem of progression. In particular we contribute with the following: (i) a major result showing that for a large class of intuitive action theories with bounded unknowns a first-order progression always exists and can be computed; (ii) a comprehensive classification of the known classes that can be progressed in first-order; (iii) a novel account of nondeterministic actions in the situation calculus.

In this paper, the fixed point semantics developed in [Lobo et al., 1992] is generalized to disjunctive logic programs with default negation and over arbitrary structures, and proved to coincide with the stable model semantics. By using the tool of ultraproducts, a preservation theorem, which asserts that a disjunctive logic program without default negation is bounded with respect to the proposed semantics if and only if it has a first-order equivalent, is then obtained. For the disjunctive logic programs with default negation, a sufficient condition assuring the first-order expressibility is also proposed.

This paper presents a new application of logic programming to a real-life problem in hydraulic engineering. The work is developed as a collaboration of computer scientists and hydraulic engineers, and applies Constraint Logic Programming to solve a hard combinatorial problem. This application deals with one aspect of the design of a water distribution network, i.e., the valve isolation system design. We take the formulation of the problem by [Giustolisi and Savic, 2008] and show how, thanks to constraint propagation, we can get better solutions than the best solution known in the literature for the Apulian distribution network.

Probabilistic logics combine the expressive power of logic with the ability to reason with uncertainty. Several probabilistic logic languages have been proposed in the past, each of them with their own features. In this paper, we propose a new probabilistic constraint logic programming language, which combines constraint logic programming with probabilistic reasoning. The language supports modeling of discrete as well as continuous probability distributions by expressing constraints on random variables. We introduce the declarative semantics of this language, present an exact inference algorithm to derive bounds on the joint probability distributions consistent with the specified constraints, and give experimental results. The results obtained are encouraging, indicating that inference in our language is feasible for solving challenging problems.

In recent years Predicate Invention has been under-explored within Inductive Logic Programming due to difficulties in formulating efficient search mechanisms. However, a recent paper demonstrated that both predicate invention and the learning of recursion can be efficiently implemented for regular and context-free grammars, by way of abduction with respect to a meta-interpreter. New predicate symbols are introduced as constants representing existentially quantified higher-order variables. In this paper we generalise the approach of Meta-Interpretive Learning (MIL) to that of learning higher-order dyadic datalog programs. We show that with an infinite signature the higher-order dyadic datalog class H 2 2 has universal Turing expressivity though H 2 2 is decidable given a finite signature. Additionally we show that Knuth-Bendix ordering of the hypothesis space together with logarithmic clause bounding allows our Dyadic MIL implementation Metagol D to PAC-learn minimal cardinailty H 2 2 definitions. This result is consistent with our experiments which indicate that Metagol D efficiently learns compact H 2 2 definitions involving predicate invention for robotic strategies and higher-order concepts in the NELL language learning domain.

We study a logical system FQHT that is appropriate for reasoning about nonmonotonic theories with intensional functions as treated in the approach of Bartholomew and Lee (2012). We provide a logical semantics, a Gentzen style proof theory and establish completeness results. The adequacy of the approach is demonstrated by showing that it captures the Bartholemew/Lee semantics and satisfies a strong equivalence property.

We define the class of e-bounded theories in the epistemic situation calculus, where the number of fluent atoms that the agent thinks may be true is bounded by a constant. Such theories can still have an infinite domain and an infinite set of states. We show that for them verification of an expressive class of first-order mu-calculus temporal epistemic properties is decidable. We also show that if the agent’s knowledge in the initial situation is e-bounded and the objective part of an action theory maintains boundedness, then the entire epistemic theory is e-bounded.

We investigate the  complexity of  satisfiability for one-agent refinement modal logic (RML), an extension of basic modal logic (ML) obtained by adding refinement quantifiers on structures.  RML is known to have the same expressiveness as ML, but the translation of RML into ML is of non-elementary complexity, and RML is at least doubly exponentially more succinct than ML. In this paper we show that RML-satisfiability is `only' singly exponentially harder than ML-satisfiability, the latter being a well-known PSPACE-complete problem.

Answer Set Programming Modulo Theories (ASPMT) is a new framework of tight integration of answer set programming (ASP) and satisfiability modulo theories (SMT). Similar to the relationship between first-order logic and SMT, it is based on a recent proposal of the functional stable model semantics by fixing interpretations of background theories. Analogously to a known relationship between ASP and SAT, "tight'' ASPMT programs can be translated into SMT instances. We demonstrate the usefulness of ASPMT by enhancing action language C+ to handle continuous changes as well as discrete changes. We reformulate the semantics of C+ in terms of ASPMT, and show that SMT solvers can be used to compute the language. We also show how the language can represent cumulative effects on continuous resources.

The action description languages B and C have significant common core. Nevertheless, some expressive possibilities of B are difficult or impossible to simulate in C, and the other way around. The main advantage of B is that it allows the user to give Prolog-style recursive definitions, which is important in applications. On the otherhand, B solves the frame problem by incorporating the commonsense law of inertia in its semantics, which makes it difficult to talk about fluents whose behavior is described by defaults other than inertia. In C and in its extension C+, the inertia assumption is expressed by axioms that the user is free to include or not to include, and other defaults can be postulated as well. This paper defines a new action description language, called BC, that combines the attractive features of B and C. Examples of formalizing commonsense domains discussed in the paper illustrate the expressive capabilities of BC and the use of answer set solvers for the automation of reasoning about actions described inthis language.